LMFDB - Embedded newform 432.2.be.c.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	432.239
Dual form			432.2.be.c.47.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36628 - 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(0.441545 + 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +O(q^{10})$	\(q+(-1.36628 - 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(0.441545 + 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +(0.0632128 + 0.358498i) q^{11} +(2.50997 - 0.913554i) q^{13} +(-2.15698 - 2.38923i) q^{15} +(2.50099 + 1.44395i) q^{17} +(2.50751 - 1.44771i) q^{19} +(-0.0430893 - 1.18900i) q^{21} +(1.39029 + 1.16659i) q^{23} +(-1.45308 - 0.528877i) q^{25} +(2.09469 - 4.75524i) q^{27} +(2.03639 - 5.59492i) q^{29} +(2.94453 - 3.50915i) q^{31} +(0.295275 - 0.557101i) q^{33} +(0.638290 + 1.10555i) q^{35} +(1.77265 - 3.07032i) q^{37} +(-4.40185 - 1.42384i) q^{39} +(3.29740 + 9.05952i) q^{41} +(11.8245 - 2.08497i) q^{43} +(0.403559 + 5.56059i) q^{45} +(-7.61569 + 6.39032i) q^{47} +(1.13360 - 6.42896i) q^{49} +(-1.87989 - 4.63529i) q^{51} -1.01980i q^{53} +0.676511i q^{55} +(-4.96713 - 0.691413i) q^{57} +(-0.864840 + 4.90475i) q^{59} +(-9.61210 + 8.06551i) q^{61} +(-1.20689 + 1.67038i) q^{63} +(4.88848 - 0.861972i) q^{65} +(-1.71306 - 4.70659i) q^{67} +(-0.657619 - 3.07394i) q^{69} +(-8.29859 + 14.3736i) q^{71} +(-6.84801 - 11.8611i) q^{73} +(1.42229 + 2.26948i) q^{75} +(-0.160735 + 0.191556i) q^{77} +(-2.52383 + 6.93417i) q^{79} +(-7.92415 + 4.26706i) q^{81} +(-3.65593 - 1.33065i) q^{83} +(4.11127 + 3.44977i) q^{85} +(-8.73839 + 5.47637i) q^{87} +(-12.1121 + 6.99291i) q^{89} +(1.58899 + 0.917403i) q^{91} +(-7.75874 + 1.65986i) q^{93} +(5.05636 - 1.84037i) q^{95} +(-0.204961 - 1.16239i) q^{97} +(-0.996494 + 0.446818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.36628	−	1.06456i	−0.788821	−	0.614623i
$3$	−1.36628	−	1.06456i	−0.788821	−	0.614623i
$4$		0			0
$5$	1.83017	+	0.322709i	0.818477	+	0.144320i	0.567184	−	0.823591i	$-0.308033\pi$
$5$	1.83017	+	0.322709i	0.818477	+	0.144320i	0.251294	+	0.967911i	$0.419144\pi$
$6$		0			0
$7$	0.441545	+	0.526213i	0.166888	+	0.198890i	0.843006	−	0.537903i	$-0.180784\pi$
$7$	0.441545	+	0.526213i	0.166888	+	0.198890i	−0.676118	+	0.736793i	$0.736339\pi$
$8$		0			0
$9$	0.733433	+	2.90896i	0.244478	+	0.969655i
$10$		0			0
$11$	0.0632128	+	0.358498i	0.0190594	+	0.108091i	0.992853	−	0.119341i	$-0.0380782\pi$
$11$	0.0632128	+	0.358498i	0.0190594	+	0.108091i	−0.973794	+	0.227432i	$0.926967\pi$
$12$		0			0
$13$	2.50997	−	0.913554i	0.696140	−	0.253374i	0.0303782	−	0.999538i	$-0.490329\pi$
$13$	2.50997	−	0.913554i	0.696140	−	0.253374i	0.665762	+	0.746164i	$0.268107\pi$
$14$		0			0
$15$	−2.15698	−	2.38923i	−0.556930	−	0.616897i
$16$		0			0
$17$	2.50099	+	1.44395i	0.606580	+	0.350209i	0.771626	−	0.636077i	$-0.219444\pi$
$17$	2.50099	+	1.44395i	0.606580	+	0.350209i	−0.165046	+	0.986286i	$0.552777\pi$
$18$		0			0
$19$	2.50751	−	1.44771i	0.575262	−	0.332128i	−0.183986	−	0.982929i	$-0.558900\pi$
$19$	2.50751	−	1.44771i	0.575262	−	0.332128i	0.759248	+	0.650801i	$0.225567\pi$
$20$		0			0
$21$	−0.0430893	−	1.18900i	−0.00940286	−	0.259462i
$22$		0			0
$23$	1.39029	+	1.16659i	0.289896	+	0.243252i	0.776124	−	0.630580i	$-0.217183\pi$
$23$	1.39029	+	1.16659i	0.289896	+	0.243252i	−0.486228	+	0.873832i	$0.661628\pi$
$24$		0			0
$25$	−1.45308	−	0.528877i	−0.290616	−	0.105775i
$26$		0			0
$27$	2.09469	−	4.75524i	0.403123	−	0.915146i
$28$		0			0
$29$	2.03639	−	5.59492i	0.378147	−	1.03895i	−0.593976	−	0.804482i	$-0.702443\pi$
$29$	2.03639	−	5.59492i	0.378147	−	1.03895i	0.972124	−	0.234469i	$-0.0753350\pi$
$30$		0			0
$31$	2.94453	−	3.50915i	0.528853	−	0.630262i	−0.433797	−	0.901011i	$-0.642827\pi$
$31$	2.94453	−	3.50915i	0.528853	−	0.630262i	0.962650	+	0.270748i	$0.0872710\pi$
$32$		0			0
$33$	0.295275	−	0.557101i	0.0514008	−	0.0969788i
$34$		0			0
$35$	0.638290	+	1.10555i	0.107891	+	0.186872i
$36$		0			0
$37$	1.77265	−	3.07032i	0.291422	−	0.504757i	−0.682725	−	0.730676i	$-0.739205\pi$
$37$	1.77265	−	3.07032i	0.291422	−	0.504757i	0.974146	+	0.225919i	$0.0725384\pi$
$38$		0			0
$39$	−4.40185	−	1.42384i	−0.704860	−	0.227997i
$40$		0			0
$41$	3.29740	+	9.05952i	0.514967	+	1.41486i	0.876002	+	0.482308i	$0.160201\pi$
$41$	3.29740	+	9.05952i	0.514967	+	1.41486i	−0.361035	+	0.932552i	$0.617577\pi$
$42$		0			0
$43$	11.8245	−	2.08497i	1.80322	−	0.317956i	0.831753	−	0.555146i	$-0.187338\pi$
$43$	11.8245	−	2.08497i	1.80322	−	0.317956i	0.971463	+	0.237190i	$0.0762264\pi$
$44$		0			0
$45$	0.403559	+	5.56059i	0.0601591	+	0.828923i
$46$		0			0
$47$	−7.61569	+	6.39032i	−1.11086	+	0.932124i	−0.998107	−	0.0614989i	$-0.980412\pi$
$47$	−7.61569	+	6.39032i	−1.11086	+	0.932124i	−0.112755	+	0.993623i	$0.535967\pi$
$48$		0			0
$49$	1.13360	−	6.42896i	0.161943	−	0.918423i
$50$		0			0
$51$	−1.87989	−	4.63529i	−0.263237	−	0.649070i
$52$		0			0
$53$		−	1.01980i		−	0.140081i	−0.997544	−	0.0700403i	$-0.977687\pi$
$53$		−	1.01980i		−	0.140081i	0.997544	−	0.0700403i	$-0.0223128\pi$
$54$		0			0
$55$			0.676511i			0.0912207i
$56$		0			0
$57$	−4.96713	−	0.691413i	−0.657913	−	0.0915799i
$58$		0			0
$59$	−0.864840	+	4.90475i	−0.112593	+	0.638544i	0.875321	+	0.483541i	$0.160650\pi$
$59$	−0.864840	+	4.90475i	−0.112593	+	0.638544i	−0.987914	+	0.155003i	$0.950461\pi$
$60$		0			0
$61$	−9.61210	+	8.06551i	−1.23070	+	1.03268i	−0.232510	+	0.972594i	$0.574694\pi$
$61$	−9.61210	+	8.06551i	−1.23070	+	1.03268i	−0.998193	+	0.0600881i	$0.980862\pi$
$62$		0			0
$63$	−1.20689	+	1.67038i	−0.152054	+	0.210448i
$64$		0			0
$65$	4.88848	−	0.861972i	0.606342	−	0.106914i
$66$		0			0
$67$	−1.71306	−	4.70659i	−0.209283	−	0.575001i	0.789990	−	0.613120i	$-0.210086\pi$
$67$	−1.71306	−	4.70659i	−0.209283	−	0.575001i	−0.999273	+	0.0381187i	$0.987863\pi$
$68$		0			0
$69$	−0.657619	−	3.07394i	−0.0791681	−	0.370059i
$70$		0			0
$71$	−8.29859	+	14.3736i	−0.984862	+	1.70583i	−0.342312	+	0.939586i	$0.611210\pi$
$71$	−8.29859	+	14.3736i	−0.984862	+	1.70583i	−0.642549	+	0.766244i	$0.722123\pi$
$72$		0			0
$73$	−6.84801	−	11.8611i	−0.801499	−	1.38824i	−0.918629	−	0.395120i	$-0.870703\pi$
$73$	−6.84801	−	11.8611i	−0.801499	−	1.38824i	0.117131	−	0.993117i	$-0.462630\pi$
$74$		0			0
$75$	1.42229	+	2.26948i	0.164232	+	0.262057i
$76$		0			0
$77$	−0.160735	+	0.191556i	−0.0183174	+	0.0218299i
$78$		0			0
$79$	−2.52383	+	6.93417i	−0.283953	+	0.780155i	0.712928	+	0.701237i	$0.247369\pi$
$79$	−2.52383	+	6.93417i	−0.283953	+	0.780155i	−0.996881	+	0.0789179i	$0.974854\pi$
$80$		0			0
$81$	−7.92415	+	4.26706i	−0.880461	+	0.474118i
$82$		0			0
$83$	−3.65593	−	1.33065i	−0.401291	−	0.146058i	0.133487	−	0.991051i	$-0.457383\pi$
$83$	−3.65593	−	1.33065i	−0.401291	−	0.146058i	−0.534778	+	0.844993i	$0.679605\pi$
$84$		0			0
$85$	4.11127	+	3.44977i	0.445930	+	0.374180i
$86$		0			0
$87$	−8.73839	+	5.47637i	−0.936854	+	0.587129i
$88$		0			0
$89$	−12.1121	+	6.99291i	−1.28388	+	0.741247i	−0.977555	−	0.210680i	$-0.932432\pi$
$89$	−12.1121	+	6.99291i	−1.28388	+	0.741247i	−0.306323	+	0.951928i	$0.599099\pi$
$90$		0			0
$91$	1.58899	+	0.917403i	0.166571	+	0.0961700i
$92$		0			0
$93$	−7.75874	+	1.65986i	−0.804544	+	0.172119i
$94$		0			0
$95$	5.05636	−	1.84037i	0.518772	−	0.188818i
$96$		0			0
$97$	−0.204961	−	1.16239i	−0.0208106	−	0.118023i	0.972633	−	0.232348i	$-0.0746407\pi$
$97$	−0.204961	−	1.16239i	−0.0208106	−	0.118023i	−0.993443	+	0.114325i	$0.963530\pi$
$98$		0			0
$99$	−0.996494	+	0.446818i	−0.100151	+	0.0449069i
$100$		0			0
$101$	−4.52719	−	5.39529i	−0.450472	−	0.536851i	0.492240	−	0.870460i	$-0.336178\pi$
$101$	−4.52719	−	5.39529i	−0.450472	−	0.536851i	−0.942712	+	0.333608i	$0.891734\pi$
$102$		0			0
$103$	9.09521	+	1.60373i	0.896178	+	0.158020i	0.602721	−	0.797952i	$-0.294083\pi$
$103$	9.09521	+	1.60373i	0.896178	+	0.158020i	0.293457	+	0.955972i	$0.405194\pi$
$104$		0			0
$105$	0.304841	−	2.18999i	0.0297494	−	0.213721i
$106$		0			0
$107$	11.7246			1.13346			0.566730	−	0.823904i	$-0.308208\pi$
$107$	11.7246			1.13346			0.566730	+	0.823904i	$0.308208\pi$
$108$		0			0
$109$	−12.7988			−1.22590			−0.612951	−	0.790121i	$-0.710018\pi$
$109$	−12.7988			−1.22590			−0.612951	+	0.790121i	$0.710018\pi$
$110$		0			0
$111$	−5.69046	+	2.30782i	−0.540115	+	0.219049i
$112$		0			0
$113$	11.2080	+	1.97627i	1.05436	+	0.185912i	0.673851	−	0.738867i	$-0.264639\pi$
$113$	11.2080	+	1.97627i	1.05436	+	0.185912i	0.380506	+	0.924779i	$0.375750\pi$
$114$		0			0
$115$	2.16800	+	2.58372i	0.202167	+	0.240934i
$116$		0			0
$117$	4.49839	+	6.63138i	0.415876	+	0.613071i
$118$		0			0
$119$	0.344477	+	1.95362i	0.0315781	+	0.179088i
$120$		0			0
$121$	10.2121	−	3.71690i	0.928372	−	0.337900i
$122$		0			0
$123$	5.13923	−	15.8881i	0.463388	−	1.43258i
$124$		0			0
$125$	−10.5358	−	6.08287i	−0.942354	−	0.544068i
$126$		0			0
$127$	−10.3478	+	5.97431i	−0.918220	+	0.530135i	−0.883067	−	0.469247i	$-0.844525\pi$
$127$	−10.3478	+	5.97431i	−0.918220	+	0.530135i	−0.0351532	+	0.999382i	$0.511192\pi$
$128$		0			0
$129$	−18.3751	−	9.73919i	−1.61784	−	0.857488i
$130$		0			0
$131$	−0.871001	−	0.730857i	−0.0760998	−	0.0638553i	0.603944	−	0.797027i	$-0.293595\pi$
$131$	−0.871001	−	0.730857i	−0.0760998	−	0.0638553i	−0.680044	+	0.733171i	$0.738039\pi$
$132$		0			0
$133$	1.86898	+	0.680255i	0.162062	+	0.0589856i
$134$		0			0
$135$	5.36819	−	8.02692i	0.462021	−	0.690848i
$136$		0			0
$137$	2.75201	−	7.56110i	0.235120	−	0.645988i	−0.764878	−	0.644175i	$-0.777201\pi$
$137$	2.75201	−	7.56110i	0.235120	−	0.645988i	0.999998	−	0.00181278i	$-0.000577027\pi$
$138$		0			0
$139$	3.48845	−	4.15737i	0.295886	−	0.352623i	−0.597535	−	0.801843i	$-0.703853\pi$
$139$	3.48845	−	4.15737i	0.295886	−	0.352623i	0.893422	+	0.449219i	$0.148298\pi$
$140$		0			0
$141$	17.2080	−	0.623615i	1.44918	−	0.0525179i
$142$		0			0
$143$	0.486169	+	0.842069i	0.0406555	+	0.0704174i
$144$		0			0
$145$	5.53246	−	9.58251i	0.459446	−	0.795784i
$146$		0			0
$147$	−8.39281	+	7.57697i	−0.692228	+	0.624938i
$148$		0			0
$149$	0.679944	+	1.86813i	0.0557032	+	0.153043i	0.964423	−	0.264363i	$-0.0851616\pi$
$149$	0.679944	+	1.86813i	0.0557032	+	0.153043i	−0.908720	+	0.417406i	$0.862939\pi$
$150$		0			0
$151$	2.82458	−	0.498049i	0.229861	−	0.0405307i	−0.0575312	−	0.998344i	$-0.518323\pi$
$151$	2.82458	−	0.498049i	0.229861	−	0.0405307i	0.287392	+	0.957813i	$0.407212\pi$
$152$		0			0
$153$	−2.36609	+	8.33434i	−0.191287	+	0.673792i
$154$		0			0
$155$	6.52142	−	5.47212i	0.523813	−	0.439532i
$156$		0			0
$157$	−2.10204	+	11.9213i	−0.167761	+	0.951421i	0.778411	+	0.627756i	$0.216026\pi$
$157$	−2.10204	+	11.9213i	−0.167761	+	0.951421i	−0.946172	+	0.323665i	$0.895085\pi$
$158$		0			0
$159$	−1.08564	+	1.39333i	−0.0860968	+	0.110499i
$160$		0			0
$161$			1.24669i			0.0982532i
$162$		0			0
$163$			3.69079i			0.289085i	0.989499	+	0.144543i	$0.0461710\pi$
$163$			3.69079i			0.289085i	−0.989499	+	0.144543i	$0.953829\pi$
$164$		0			0
$165$	0.720185	−	0.924302i	0.0560663	−	0.0719568i
$166$		0			0
$167$	3.60391	−	20.4388i	0.278879	−	1.58160i	−0.447487	−	0.894291i	$-0.647681\pi$
$167$	3.60391	−	20.4388i	0.278879	−	1.58160i	0.726365	−	0.687309i	$-0.241208\pi$
$168$		0			0
$169$	−4.49321	+	3.77025i	−0.345632	+	0.290020i
$170$		0			0
$171$	6.05043	+	6.23246i	0.462688	+	0.476608i
$172$		0			0
$173$	6.14247	−	1.08308i	0.467003	−	0.0823452i	0.0648051	−	0.997898i	$-0.479357\pi$
$173$	6.14247	−	1.08308i	0.467003	−	0.0823452i	0.402198	+	0.915553i	$0.368246\pi$
$174$		0			0
$175$	−0.363298	−	0.998152i	−0.0274627	−	0.0754532i
$176$		0			0
$177$	6.40300	−	5.78058i	0.481279	−	0.434495i
$178$		0			0
$179$	−6.76734	+	11.7214i	−0.505815	+	0.876097i	0.494163	+	0.869369i	$0.335475\pi$
$179$	−6.76734	+	11.7214i	−0.505815	+	0.876097i	−0.999977	+	0.00672715i	$0.997859\pi$
$180$		0			0
$181$	−3.39270	−	5.87633i	−0.252177	−	0.436784i	0.711948	−	0.702232i	$-0.247813\pi$
$181$	−3.39270	−	5.87633i	−0.252177	−	0.436784i	−0.964125	+	0.265449i	$0.914480\pi$
$182$		0			0
$183$	21.7190	−	0.787093i	1.60551	−	0.0581836i
$184$		0			0
$185$	4.23507	−	5.04715i	0.311368	−	0.371074i
$186$		0			0
$187$	−0.359557	+	0.987876i	−0.0262934	+	0.0722406i
$188$		0			0
$189$	3.42717	−	0.997400i	0.249290	−	0.0725502i
$190$		0			0
$191$	−15.3682	−	5.59358i	−1.11201	−	0.404737i	−0.280278	−	0.959919i	$-0.590427\pi$
$191$	−15.3682	−	5.59358i	−1.11201	−	0.404737i	−0.831729	+	0.555181i	$0.812649\pi$
$192$		0			0
$193$	14.5207	+	12.1843i	1.04522	+	0.877046i	0.992583	−	0.121568i	$-0.0387922\pi$
$193$	14.5207	+	12.1843i	1.04522	+	0.877046i	0.0526393	+	0.998614i	$0.483237\pi$
$194$		0			0
$195$	−7.59665	−	4.02638i	−0.544007	−	0.288335i
$196$		0			0
$197$	−20.4041	+	11.7803i	−1.45373	+	0.839312i	−0.998691	−	0.0511593i	$-0.983708\pi$
$197$	−20.4041	+	11.7803i	−1.45373	+	0.839312i	−0.455040	+	0.890471i	$0.650375\pi$
$198$		0			0
$199$	−10.8690	−	6.27522i	−0.770482	−	0.444838i	0.0625642	−	0.998041i	$-0.480072\pi$
$199$	−10.8690	−	6.27522i	−0.770482	−	0.444838i	−0.833047	+	0.553203i	$0.813406\pi$
$200$		0			0
$201$	−2.66992	+	8.25416i	−0.188322	+	0.582203i
$202$		0			0
$203$	3.84328	−	1.39884i	0.269745	−	0.0981792i
$204$		0			0
$205$	3.11121	+	17.6446i	0.217297	+	1.23235i
$206$		0			0
$207$	−2.37389	+	4.89993i	−0.164997	+	0.340569i
$208$		0			0
$209$	0.677508	+	0.807423i	0.0468642	+	0.0558506i
$210$		0			0
$211$	−19.5778	−	3.45209i	−1.34779	−	0.237652i	−0.547269	−	0.836957i	$-0.684332\pi$
$211$	−19.5778	−	3.45209i	−1.34779	−	0.237652i	−0.800520	+	0.599305i	$0.795444\pi$
$212$		0			0
$213$	26.6397	−	10.8040i	1.82532	−	0.740277i
$214$		0			0
$215$	22.3137			1.52178
$216$		0			0
$217$	3.14670			0.213612
$218$		0			0
$219$	−3.27054	+	23.4957i	−0.221003	+	1.58769i
$220$		0			0
$221$	7.59654	+	1.33948i	0.510999	+	0.0901029i
$222$		0			0
$223$	−5.80196	−	6.91450i	−0.388528	−	0.463029i	0.535959	−	0.844244i	$-0.319950\pi$
$223$	−5.80196	−	6.91450i	−0.388528	−	0.463029i	−0.924486	+	0.381215i	$0.875506\pi$
$224$		0			0
$225$	0.472750	−	4.61485i	0.0315167	−	0.307657i
$226$		0			0
$227$	−2.31547	−	13.1317i	−0.153683	−	0.871579i	−0.959980	−	0.280068i	$-0.909643\pi$
$227$	−2.31547	−	13.1317i	−0.153683	−	0.871579i	0.806297	−	0.591511i	$-0.201468\pi$
$228$		0			0
$229$	8.54248	−	3.10921i	0.564503	−	0.205462i	−0.0439755	−	0.999033i	$-0.514002\pi$
$229$	8.54248	−	3.10921i	0.564503	−	0.205462i	0.608479	+	0.793570i	$0.291780\pi$
$230$		0			0
$231$	0.423531	−	0.0906077i	0.0278663	−	0.00596155i
$232$		0			0
$233$	6.17144	+	3.56308i	0.404304	+	0.233425i	0.688340	−	0.725389i	$-0.258340\pi$
$233$	6.17144	+	3.56308i	0.404304	+	0.233425i	−0.284035	+	0.958814i	$0.591673\pi$
$234$		0			0
$235$	−16.0002	+	9.23773i	−1.04374	+	0.602603i
$236$		0			0
$237$	10.8301	−	6.78724i	0.703490	−	0.440879i
$238$		0			0
$239$	−6.43186	−	5.39697i	−0.416042	−	0.349101i	0.410613	−	0.911810i	$-0.365315\pi$
$239$	−6.43186	−	5.39697i	−0.416042	−	0.349101i	−0.826655	+	0.562709i	$0.809759\pi$
$240$		0			0
$241$	7.89267	+	2.87270i	0.508412	+	0.185047i	0.583474	−	0.812132i	$-0.301693\pi$
$241$	7.89267	+	2.87270i	0.508412	+	0.185047i	−0.0750618	+	0.997179i	$0.523915\pi$
$242$		0			0
$243$	15.3691	+	2.60573i	0.985930	+	0.167158i
$244$		0			0
$245$	4.14936	−	11.4003i	0.265093	−	0.728337i
$246$		0			0
$247$	4.97121	−	5.92446i	0.316311	−	0.376964i
$248$		0			0
$249$	3.57847	+	5.70999i	0.226776	+	0.361856i
$250$		0			0
$251$	−15.6479	−	27.1030i	−0.987688	−	1.71073i	−0.629322	−	0.777145i	$-0.716667\pi$
$251$	−15.6479	−	27.1030i	−0.987688	−	1.71073i	−0.358366	−	0.933581i	$-0.616666\pi$
$252$		0			0
$253$	−0.330337	+	0.572160i	−0.0207681	+	0.0359714i
$254$		0			0
$255$	−1.94466	−	9.09003i	−0.121780	−	0.569240i
$256$		0			0
$257$	7.17068	+	19.7013i	0.447295	+	1.22893i	0.934600	+	0.355700i	$0.115758\pi$
$257$	7.17068	+	19.7013i	0.447295	+	1.22893i	−0.487305	+	0.873232i	$0.662020\pi$
$258$		0			0
$259$	2.39834	−	0.422893i	0.149026	−	0.0262773i
$260$		0			0
$261$	17.7690	+	1.82027i	1.09987	+	0.112672i
$262$		0			0
$263$	5.60982	−	4.70720i	0.345916	−	0.290258i	−0.453231	−	0.891393i	$-0.649729\pi$
$263$	5.60982	−	4.70720i	0.345916	−	0.290258i	0.799148	+	0.601135i	$0.205284\pi$
$264$		0			0
$265$	0.329099	−	1.86641i	0.0202164	−	0.114653i
$266$		0			0
$267$	23.9928	+	3.33975i	1.46834	+	0.204389i
$268$		0			0
$269$		−	18.3626i		−	1.11959i	−0.828632	−	0.559793i	$-0.810880\pi$
$269$		−	18.3626i		−	1.11959i	0.828632	−	0.559793i	$-0.189120\pi$
$270$		0			0
$271$		−	1.08071i		−	0.0656483i	−0.999461	−	0.0328241i	$-0.989550\pi$
$271$		−	1.08071i		−	0.0656483i	0.999461	−	0.0328241i	$-0.0104501\pi$
$272$		0			0
$273$	−1.19437	−	2.94500i	−0.0722867	−	0.178239i
$274$		0			0
$275$	0.0977481	−	0.554357i	0.00589443	−	0.0334290i
$276$		0			0
$277$	−10.6528	+	8.93879i	−0.640067	+	0.537080i	−0.904039	−	0.427450i	$-0.859412\pi$
$277$	−10.6528	+	8.93879i	−0.640067	+	0.537080i	0.263972	+	0.964530i	$0.414967\pi$
$278$		0			0
$279$	12.3676	+	5.99180i	0.740430	+	0.358720i
$280$		0			0
$281$	5.52866	−	0.974852i	0.329812	−	0.0581548i	−0.00629033	−	0.999980i	$-0.502002\pi$
$281$	5.52866	−	0.974852i	0.329812	−	0.0581548i	0.336102	+	0.941825i	$0.390891\pi$
$282$		0			0
$283$	−5.59448	−	15.3707i	−0.332558	−	0.913694i	−0.987444	−	0.157967i	$-0.949506\pi$
$283$	−5.59448	−	15.3707i	−0.332558	−	0.913694i	0.654887	−	0.755727i	$-0.272716\pi$
$284$		0			0
$285$	−8.86757	−	2.86834i	−0.525270	−	0.169906i
$286$		0			0
$287$	−3.31129	+	5.73532i	−0.195459	+	0.338545i
$288$		0			0
$289$	−4.33002	−	7.49982i	−0.254707	−	0.441166i
$290$		0			0
$291$	−0.957398	+	1.80634i	−0.0561237	+	0.105890i
$292$		0			0
$293$	−7.32574	+	8.73048i	−0.427975	+	0.510040i	−0.936337	−	0.351103i	$-0.885807\pi$
$293$	−7.32574	+	8.73048i	−0.427975	+	0.510040i	0.508362	+	0.861143i	$0.330251\pi$
$294$		0			0
$295$	−3.16561	+	8.69744i	−0.184309	+	0.506385i
$296$		0			0
$297$	1.83715	+	0.450349i	0.106602	+	0.0261319i
$298$		0			0
$299$	4.55534	+	1.65801i	0.263442	+	0.0958850i
$300$		0			0
$301$	6.31818	+	5.30159i	0.364174	+	0.305578i
$302$		0			0
$303$	0.441797	+	12.1909i	0.0253806	+	0.700350i
$304$		0			0
$305$	−20.1946	+	11.6593i	−1.15634	+	0.667612i
$306$		0			0
$307$	−6.20934	−	3.58496i	−0.354386	−	0.204605i	0.312230	−	0.950007i	$-0.398924\pi$
$307$	−6.20934	−	3.58496i	−0.354386	−	0.204605i	−0.666615	+	0.745402i	$0.732258\pi$
$308$		0			0
$309$	−10.7193	−	11.8735i	−0.609801	−	0.675461i
$310$		0			0
$311$	20.1437	−	7.33171i	1.14224	−	0.415743i	0.299521	−	0.954090i	$-0.403173\pi$
$311$	20.1437	−	7.33171i	1.14224	−	0.415743i	0.842723	+	0.538347i	$0.180951\pi$
$312$		0			0
$313$	1.26646	+	7.18245i	0.0715845	+	0.405976i	0.999453	+	0.0330687i	$0.0105280\pi$
$313$	1.26646	+	7.18245i	0.0715845	+	0.405976i	−0.927869	+	0.372907i	$0.878361\pi$
$314$		0			0
$315$	−2.74786	+	2.66761i	−0.154825	+	0.150303i
$316$		0			0
$317$	−14.9507	−	17.8176i	−0.839717	−	1.00074i	−0.999907	−	0.0136497i	$-0.995655\pi$
$317$	−14.9507	−	17.8176i	−0.839717	−	1.00074i	0.160190	−	0.987086i	$-0.448789\pi$
$318$		0			0
$319$	2.13449	+	0.376368i	0.119509	+	0.0210726i
$320$		0			0
$321$	−16.0191	−	12.4815i	−0.894097	−	0.696650i
$322$		0			0
$323$	8.36169			0.465257
$324$		0			0
$325$	−4.13034			−0.229110
$326$		0			0
$327$	17.4867	+	13.6251i	0.967018	+	0.753467i
$328$		0			0
$329$	−6.72534	−	1.18586i	−0.370780	−	0.0653785i
$330$		0			0
$331$	7.44461	+	8.87214i	0.409193	+	0.487657i	0.930800	−	0.365529i	$-0.119112\pi$
$331$	7.44461	+	8.87214i	0.409193	+	0.487657i	−0.521607	+	0.853186i	$0.674667\pi$
$332$		0			0
$333$	10.2316	+	2.90470i	0.560686	+	0.159177i
$334$		0			0
$335$	−1.61633	−	9.16668i	−0.0883097	−	0.500829i
$336$		0			0
$337$	9.71533	−	3.53609i	0.529228	−	0.192623i	−0.0635658	−	0.997978i	$-0.520247\pi$
$337$	9.71533	−	3.53609i	0.529228	−	0.192623i	0.592793	+	0.805355i	$0.298025\pi$
$338$		0			0
$339$	−13.2094	−	14.6317i	−0.717434	−	0.794683i
$340$		0			0
$341$	1.44415	+	0.833783i	0.0782053	+	0.0451519i
$342$		0			0
$343$	8.04778	−	4.64639i	0.434540	−	0.250882i
$344$		0			0
$345$	−0.211570	−	5.83805i	−0.0113905	−	0.314310i
$346$		0			0
$347$	9.93967	+	8.34038i	0.533590	+	0.447735i	0.869339	−	0.494217i	$-0.164545\pi$
$347$	9.93967	+	8.34038i	0.533590	+	0.447735i	−0.335749	+	0.941951i	$0.608989\pi$
$348$		0			0
$349$	−18.4970	−	6.73235i	−0.990121	−	0.360375i	−0.204354	−	0.978897i	$-0.565509\pi$
$349$	−18.4970	−	6.73235i	−0.990121	−	0.360375i	−0.785767	+	0.618522i	$0.787732\pi$
$350$		0			0
$351$	0.913437	−	13.8491i	0.0487557	−	0.739211i
$352$		0			0
$353$	−1.12185	+	3.08225i	−0.0597099	+	0.164052i	−0.965961	−	0.258689i	$-0.916710\pi$
$353$	−1.12185	+	3.08225i	−0.0597099	+	0.164052i	0.906251	+	0.422740i	$0.138932\pi$
$354$		0			0
$355$	−19.8263	+	23.6281i	−1.05227	+	1.25405i
$356$		0			0
$357$	1.60910	−	3.03591i	0.0851624	−	0.160677i
$358$		0			0
$359$	−4.91834	−	8.51881i	−0.259580	−	0.449606i	0.706549	−	0.707664i	$-0.250251\pi$
$359$	−4.91834	−	8.51881i	−0.259580	−	0.449606i	−0.966129	+	0.258058i	$0.916917\pi$
$360$		0			0
$361$	−5.30826	+	9.19417i	−0.279382	+	0.483904i
$362$		0			0
$363$	−17.9094	−	5.79305i	−0.940001	−	0.304056i
$364$		0			0
$365$	−8.70535	−	23.9177i	−0.455659	−	1.25191i
$366$		0			0
$367$	−28.4143	+	5.01021i	−1.48321	+	0.261531i	−0.855862	−	0.517205i	$-0.826973\pi$
$367$	−28.4143	+	5.01021i	−1.48321	+	0.261531i	−0.627352	+	0.778735i	$0.715861\pi$
$368$		0			0
$369$	−23.9354	+	16.2366i	−1.24603	+	0.845242i
$370$		0			0
$371$	0.536634	−	0.450289i	0.0278606	−	0.0233778i
$372$		0			0
$373$	0.186692	−	1.05878i	0.00966652	−	0.0548216i	−0.979593	−	0.200992i	$-0.935584\pi$
$373$	0.186692	−	1.05878i	0.00966652	−	0.0548216i	0.989259	+	0.146170i	$0.0466947\pi$
$374$		0			0
$375$	7.91932	+	19.5269i	0.408952	+	1.00836i
$376$		0			0
$377$		−	15.9034i		−	0.819068i
$378$		0			0
$379$			26.9955i			1.38667i	0.720617	+	0.693333i	$0.243858\pi$
$379$			26.9955i			1.38667i	−0.720617	+	0.693333i	$0.756142\pi$
$380$		0			0
$381$	20.4980	+	2.85327i	1.05014	+	0.146178i
$382$		0			0
$383$	3.42477	−	19.4229i	0.174998	−	0.992461i	−0.763149	−	0.646223i	$-0.776348\pi$
$383$	3.42477	−	19.4229i	0.174998	−	0.992461i	0.938147	−	0.346239i	$-0.112541\pi$
$384$		0			0
$385$	−0.355989	+	0.298710i	−0.0181429	+	0.0152237i
$386$		0			0
$387$	14.7376	+	32.8678i	0.749153	+	1.67076i
$388$		0			0
$389$	−20.2544	+	3.57139i	−1.02694	+	0.181077i	−0.661646	−	0.749817i	$-0.730142\pi$
$389$	−20.2544	+	3.57139i	−1.02694	+	0.181077i	−0.365291	+	0.930893i	$0.619031\pi$
$390$		0			0
$391$	1.79261	+	4.92515i	0.0906561	+	0.249076i
$392$		0			0
$393$	0.411991	+	1.92579i	0.0207822	+	0.0971430i
$394$		0			0
$395$	−6.85676	+	11.8763i	−0.345001	+	0.597559i
$396$		0			0
$397$	11.5650	+	20.0311i	0.580430	+	1.00533i	0.995428	+	0.0955122i	$0.0304489\pi$
$397$	11.5650	+	20.0311i	0.580430	+	1.00533i	−0.414998	+	0.909822i	$0.636218\pi$
$398$		0			0
$399$	−1.82938	−	2.91906i	−0.0915837	−	0.146136i
$400$		0			0
$401$	−9.33843	+	11.1291i	−0.466339	+	0.555761i	−0.947037	−	0.321125i	$-0.895939\pi$
$401$	−9.33843	+	11.1291i	−0.466339	+	0.555761i	0.480698	+	0.876886i	$0.340383\pi$
$402$		0			0
$403$	4.18488	−	11.4979i	0.208463	−	0.572749i
$404$		0			0
$405$	−15.8796	+	5.25226i	−0.789062	+	0.260987i
$406$		0			0
$407$	1.21275	+	0.441407i	0.0601140	+	0.0218797i
$408$		0			0
$409$	−15.2899	−	12.8298i	−0.756038	−	0.634392i	0.181054	−	0.983473i	$-0.442049\pi$
$409$	−15.2899	−	12.8298i	−0.756038	−	0.634392i	−0.937092	+	0.349082i	$0.886494\pi$
$410$		0			0
$411$	−11.8092	+	7.40088i	−0.582507	+	0.365059i
$412$		0			0
$413$	−2.96281	+	1.71058i	−0.145790	+	0.0841721i
$414$		0			0
$415$	−6.26157	−	3.61512i	−0.307368	−	0.177459i
$416$		0			0
$417$	−9.19195	+	1.96647i	−0.450132	+	0.0962984i
$418$		0			0
$419$	−24.7184	+	8.99676i	−1.20757	+	0.439520i	−0.865861	−	0.500285i	$-0.833229\pi$
$419$	−24.7184	+	8.99676i	−1.20757	+	0.439520i	−0.341711	+	0.939805i	$0.611006\pi$
$420$		0			0
$421$	1.54271	+	8.74913i	0.0751870	+	0.426407i	0.999046	+	0.0436734i	$0.0139061\pi$
$421$	1.54271	+	8.74913i	0.0751870	+	0.426407i	−0.923859	+	0.382733i	$0.874983\pi$
$422$		0			0
$423$	−24.1748	−	17.4669i	−1.17542	−	0.849269i
$424$		0			0
$425$	−2.87047	−	3.42089i	−0.139238	−	0.165938i
$426$		0			0
$427$	−8.48835	−	1.49673i	−0.410780	−	0.0724316i
$428$		0			0
$429$	0.232190	−	1.66806i	0.0112102	−	0.0805345i
$430$		0			0
$431$	35.6692			1.71812			0.859062	−	0.511872i	$-0.171048\pi$
$431$	35.6692			1.71812			0.859062	+	0.511872i	$0.171048\pi$
$432$		0			0
$433$	20.3661			0.978735			0.489367	−	0.872078i	$-0.337228\pi$
$433$	20.3661			0.978735			0.489367	+	0.872078i	$0.337228\pi$
$434$		0			0
$435$	−17.7600	+	7.20274i	−0.851528	+	0.345345i
$436$		0			0
$437$	5.17506	+	0.912503i	0.247557	+	0.0436510i
$438$		0			0
$439$	21.4995	+	25.6222i	1.02612	+	1.22288i	0.974541	+	0.224209i	$0.0719800\pi$
$439$	21.4995	+	25.6222i	1.02612	+	1.22288i	0.0515759	+	0.998669i	$0.483576\pi$
$440$		0			0
$441$	19.5330	−	1.41761i	0.930145	−	0.0675052i
$442$		0			0
$443$	2.76559	+	15.6845i	0.131397	+	0.745191i	0.977301	+	0.211855i	$0.0679506\pi$
$443$	2.76559	+	15.6845i	0.131397	+	0.745191i	−0.845904	+	0.533336i	$0.820938\pi$
$444$		0			0
$445$	−24.4239	+	8.88956i	−1.15780	+	0.421405i
$446$		0			0
$447$	1.05974	−	3.27623i	0.0501240	−	0.154960i
$448$		0			0
$449$	21.6096	+	12.4763i	1.01982	+	0.588795i	0.914052	−	0.405596i	$-0.132936\pi$
$449$	21.6096	+	12.4763i	1.01982	+	0.588795i	0.105770	+	0.994391i	$0.466269\pi$
$450$		0			0
$451$	−3.03938	+	1.75479i	−0.143119	+	0.0826297i
$452$		0			0
$453$	−4.38936	−	2.32645i	−0.206230	−	0.109306i
$454$		0			0
$455$	2.61207	+	2.19178i	0.122456	+	0.102752i
$456$		0			0
$457$	−16.1920	−	5.89341i	−0.757431	−	0.275682i	−0.0657017	−	0.997839i	$-0.520929\pi$
$457$	−16.1920	−	5.89341i	−0.757431	−	0.275682i	−0.691729	+	0.722157i	$0.743151\pi$
$458$		0			0
$459$	12.1051	−	8.86819i	0.565019	−	0.413932i
$460$		0			0
$461$	2.09999	−	5.76968i	0.0978065	−	0.268721i	−0.881134	−	0.472866i	$-0.843219\pi$
$461$	2.09999	−	5.76968i	0.0978065	−	0.268721i	0.978941	+	0.204145i	$0.0654415\pi$
$462$		0			0
$463$	3.43905	−	4.09850i	0.159826	−	0.190474i	−0.680188	−	0.733038i	$-0.738102\pi$
$463$	3.43905	−	4.09850i	0.159826	−	0.190474i	0.840014	+	0.542564i	$0.182546\pi$
$464$		0			0
$465$	−14.7355	+	0.534011i	−0.683341	+	0.0247642i
$466$		0			0
$467$	−16.2724	−	28.1846i	−0.752995	−	1.30423i	−0.946365	−	0.323100i	$-0.895275\pi$
$467$	−16.2724	−	28.1846i	−0.752995	−	1.30423i	0.193370	−	0.981126i	$-0.438058\pi$
$468$		0			0
$469$	1.72028	−	2.97960i	0.0794349	−	0.137585i
$470$		0			0
$471$	15.5629	−	14.0500i	0.717098	−	0.647391i
$472$		0			0
$473$	1.49492	+	4.10725i	0.0687363	+	0.188852i
$474$		0			0
$475$	−4.40927	+	0.777474i	−0.202311	+	0.0356729i
$476$		0			0
$477$	2.96657	−	0.747957i	0.135830	−	0.0342466i
$478$		0			0
$479$	−31.7640	+	26.6531i	−1.45133	+	1.21781i	−0.519732	+	0.854330i	$0.673968\pi$
$479$	−31.7640	+	26.6531i	−1.45133	+	1.21781i	−0.931601	+	0.363483i	$0.881587\pi$
$480$		0			0
$481$	1.64439	−	9.32581i	0.0749778	−	0.425220i
$482$		0			0
$483$	1.32718	−	1.70333i	0.0603887	−	0.0775042i
$484$		0			0
$485$		−	2.19352i		−	0.0996024i
$486$		0			0
$487$		−	40.8059i		−	1.84909i	−0.381072	−	0.924545i	$-0.624445\pi$
$487$		−	40.8059i		−	1.84909i	0.381072	−	0.924545i	$-0.375555\pi$
$488$		0			0
$489$	3.92906	−	5.04265i	0.177678	−	0.228036i
$490$		0			0
$491$	−4.86890	+	27.6129i	−0.219730	+	1.24615i	0.652777	+	0.757550i	$0.273604\pi$
$491$	−4.86890	+	27.6129i	−0.219730	+	1.24615i	−0.872507	+	0.488602i	$0.837507\pi$
$492$		0			0
$493$	13.1718	−	11.0524i	0.593227	−	0.497776i
$494$		0			0
$495$	−1.96795	+	0.496175i	−0.0884526	+	0.0223014i
$496$		0			0
$497$	−11.2278	+	1.97976i	−0.503634	+	0.0888043i
$498$		0			0
$499$	3.37784	+	9.28054i	0.151213	+	0.415454i	0.992052	−	0.125832i	$-0.0401600\pi$
$499$	3.37784	+	9.28054i	0.151213	+	0.415454i	−0.840839	+	0.541286i	$0.817938\pi$
$500$		0			0
$501$	−26.6822	+	24.0885i	−1.19207	+	1.07619i
$502$		0			0
$503$	−12.4724	+	21.6029i	−0.556117	+	0.963224i	0.441698	+	0.897164i	$0.354376\pi$
$503$	−12.4724	+	21.6029i	−0.556117	+	0.963224i	−0.997816	+	0.0660600i	$0.978957\pi$
$504$		0			0
$505$	−6.54442	−	11.3353i	−0.291223	−	0.504413i
$506$		0			0
$507$	10.1526	−	0.367930i	0.450894	−	0.0163403i
$508$		0			0
$509$	−4.22498	+	5.03513i	−0.187269	+	0.223178i	−0.851508	−	0.524342i	$-0.824311\pi$
$509$	−4.22498	+	5.03513i	−0.187269	+	0.223178i	0.664239	+	0.747520i	$0.268756\pi$
$510$		0			0
$511$	3.21776	−	8.84072i	0.142345	−	0.391091i
$512$		0			0
$513$	−1.63176	−	14.9563i	−0.0720440	−	0.660337i
$514$		0			0
$515$	16.1283	+	5.87020i	0.710696	+	0.258672i
$516$		0			0
$517$	−2.77232	−	2.32625i	−0.121927	−	0.102309i
$518$		0			0
$519$	−9.54532	−	5.05922i	−0.418993	−	0.222075i
$520$		0			0
$521$	17.2065	−	9.93418i	0.753831	−	0.435224i	−0.0732458	−	0.997314i	$-0.523336\pi$
$521$	17.2065	−	9.93418i	0.753831	−	0.435224i	0.827076	+	0.562090i	$0.190002\pi$
$522$		0			0
$523$	25.5708	+	14.7633i	1.11813	+	0.645554i	0.940923	−	0.338620i	$-0.109960\pi$
$523$	25.5708	+	14.7633i	1.11813	+	0.645554i	0.177209	+	0.984173i	$0.443293\pi$
$524$		0			0
$525$	−0.566225	+	1.75051i	−0.0247121	+	0.0763983i
$526$		0			0
$527$	12.4313	−	4.52462i	0.541515	−	0.197095i
$528$		0			0
$529$	−3.42194	−	19.4068i	−0.148780	−	0.843773i
$530$		0			0
$531$	−14.9021	+	1.08152i	−0.646694	+	0.0469338i
$532$		0			0
$533$	16.5527	+	19.7268i	0.716978	+	0.854461i
$534$		0			0
$535$	21.4580	+	3.78363i	0.927711	+	0.163580i
$536$		0			0
$537$	21.7241	−	8.81043i	0.937466	−	0.380198i
$538$		0			0
$539$	2.37642			0.102360
$540$		0			0
$541$	−13.0123			−0.559444			−0.279722	−	0.960081i	$-0.590242\pi$
$541$	−13.0123			−0.559444			−0.279722	+	0.960081i	$0.590242\pi$
$542$		0			0
$543$	−1.62032	+	11.6404i	−0.0695346	+	0.499538i
$544$		0			0
$545$	−23.4240	−	4.13028i	−1.00337	−	0.176922i
$546$		0			0
$547$	−13.8628	−	16.5211i	−0.592732	−	0.706391i	0.383396	−	0.923584i	$-0.374754\pi$
$547$	−13.8628	−	16.5211i	−0.592732	−	0.706391i	−0.976129	+	0.217193i	$0.930310\pi$
$548$		0			0
$549$	−30.5121	−	22.0457i	−1.30222	−	0.940889i
$550$		0			0
$551$	−2.99358	−	16.9774i	−0.127531	−	0.723263i
$552$		0			0
$553$	−4.76324	+	1.73368i	−0.202553	+	0.0737234i
$554$		0			0
$555$	−11.1593	+	2.38735i	−0.473685	+	0.101337i
$556$		0			0
$557$	26.8521	+	15.5031i	1.13776	+	0.656886i	0.945875	−	0.324531i	$-0.105207\pi$
$557$	26.8521	+	15.5031i	1.13776	+	0.656886i	0.191885	+	0.981417i	$0.438540\pi$
$558$		0			0
$559$	27.7743	−	16.0355i	1.17473	−	0.678230i
$560$		0			0
$561$	1.54291	−	0.966944i	0.0651416	−	0.0408244i
$562$		0			0
$563$	−8.12175	−	6.81496i	−0.342291	−	0.287216i	0.455395	−	0.890290i	$-0.349498\pi$
$563$	−8.12175	−	6.81496i	−0.342291	−	0.287216i	−0.797686	+	0.603073i	$0.793943\pi$
$564$		0			0
$565$	19.8747	+	7.23382i	0.836137	+	0.304329i
$566$		0			0
$567$	−5.74425	−	2.28569i	−0.241236	−	0.0959901i
$568$		0			0
$569$	−3.42133	+	9.40004i	−0.143430	+	0.394070i	−0.990518	−	0.137382i	$-0.956131\pi$
$569$	−3.42133	+	9.40004i	−0.143430	+	0.394070i	0.847088	+	0.531452i	$0.178353\pi$
$570$		0			0
$571$	18.8465	−	22.4604i	0.788702	−	0.939938i	−0.210590	−	0.977575i	$-0.567538\pi$
$571$	18.8465	−	22.4604i	0.788702	−	0.939938i	0.999291	+	0.0376364i	$0.0119829\pi$
$572$		0			0
$573$	15.0426	+	24.0028i	0.628414	+	1.00273i
$574$		0			0
$575$	−1.40322	−	2.43045i	−0.0585182	−	0.101357i
$576$		0			0
$577$	−3.08995	+	5.35195i	−0.128636	+	0.222805i	−0.923148	−	0.384444i	$-0.874393\pi$
$577$	−3.08995	+	5.35195i	−0.128636	+	0.222805i	0.794512	+	0.607248i	$0.207727\pi$
$578$		0			0
$579$	−6.86841	−	32.1053i	−0.285441	−	1.33425i
$580$		0			0
$581$	−0.914054	−	2.51134i	−0.0379213	−	0.104188i
$582$		0			0
$583$	0.365597	−	0.0644646i	0.0151415	−	0.00266985i
$584$		0			0
$585$	6.09282	+	13.5882i	0.251907	+	0.561804i
$586$		0			0
$587$	21.4842	−	18.0274i	0.886749	−	0.744071i	−0.0808061	−	0.996730i	$-0.525749\pi$
$587$	21.4842	−	18.0274i	0.886749	−	0.744071i	0.967555	+	0.252659i	$0.0813050\pi$
$588$		0			0
$589$	2.30320	−	13.0621i	0.0949015	−	0.538213i
$590$		0			0
$591$	40.4185	+	5.62616i	1.66259	+	0.231429i
$592$		0			0
$593$		−	3.19379i		−	0.131153i	−0.997848	−	0.0655767i	$-0.979111\pi$
$593$		−	3.19379i		−	0.131153i	0.997848	−	0.0655767i	$-0.0208887\pi$
$594$		0			0
$595$			3.68663i			0.151137i
$596$		0			0
$597$	8.16974	+	20.1444i	0.334365	+	0.824454i
$598$		0			0
$599$	−4.65896	+	26.4223i	−0.190360	+	1.07958i	0.728513	+	0.685032i	$0.240212\pi$
$599$	−4.65896	+	26.4223i	−0.190360	+	1.07958i	−0.918873	+	0.394553i	$0.870899\pi$
$600$		0			0
$601$	16.5609	−	13.8962i	0.675532	−	0.566839i	−0.239165	−	0.970979i	$-0.576874\pi$
$601$	16.5609	−	13.8962i	0.675532	−	0.566839i	0.914697	+	0.404140i	$0.132429\pi$
$602$		0			0
$603$	12.4349	−	8.43519i	0.506388	−	0.343507i
$604$		0			0
$605$	19.8894	−	3.50703i	0.808617	−	0.142581i
$606$		0			0
$607$	6.00813	+	16.5072i	0.243862	+	0.670007i	0.999881	+	0.0154559i	$0.00491995\pi$
$607$	6.00813	+	16.5072i	0.243862	+	0.670007i	−0.756018	+	0.654551i	$0.772858\pi$
$608$		0			0
$609$	−6.74013	−	2.18019i	−0.273124	−	0.0883457i
$610$		0			0
$611$	−13.2772	+	22.9968i	−0.537139	+	0.930353i
$612$		0			0
$613$	13.8232	+	23.9424i	0.558313	+	0.967026i	0.997638	+	0.0686979i	$0.0218844\pi$
$613$	13.8232	+	23.9424i	0.558313	+	0.967026i	−0.439325	+	0.898328i	$0.644782\pi$
$614$		0			0
$615$	14.5329	−	27.4195i	0.586023	−	1.10566i
$616$		0			0
$617$	30.7467	−	36.6425i	1.23782	−	1.47517i	0.412046	−	0.911163i	$-0.364814\pi$
$617$	30.7467	−	36.6425i	1.23782	−	1.47517i	0.825769	−	0.564008i	$-0.190741\pi$
$618$		0			0
$619$	14.6524	−	40.2571i	0.588929	−	1.61807i	−0.183538	−	0.983013i	$-0.558755\pi$
$619$	14.6524	−	40.2571i	0.588929	−	1.61807i	0.772467	−	0.635055i	$-0.219023\pi$
$620$		0			0
$621$	8.45966	−	4.16752i	0.339474	−	0.167237i
$622$		0			0
$623$	−9.02779	−	3.28585i	−0.361691	−	0.131645i
$624$		0			0
$625$	−11.3966	−	9.56287i	−0.455863	−	0.382515i
$626$		0			0
$627$	−0.0661163	−	1.82441i	−0.00264043	−	0.0728599i
$628$		0			0
$629$	8.86676	−	5.11923i	0.353541	−	0.204117i
$630$		0			0
$631$	−6.97385	−	4.02635i	−0.277625	−	0.160287i	0.354723	−	0.934971i	$-0.384575\pi$
$631$	−6.97385	−	4.02635i	−0.277625	−	0.160287i	−0.632348	+	0.774685i	$0.717909\pi$
$632$		0			0
$633$	23.0737	+	25.5582i	0.917099	+	1.01585i
$634$		0			0
$635$	−20.8662	+	7.59469i	−0.828051	+	0.301386i
$636$		0			0
$637$	−3.02790	−	17.1721i	−0.119970	−	0.680383i
$638$		0			0
$639$	−47.8987	−	13.5983i	−1.89484	−	0.537939i
$640$		0			0
$641$	29.9247	+	35.6629i	1.18195	+	1.40860i	0.892286	+	0.451471i	$0.149101\pi$
$641$	29.9247	+	35.6629i	1.18195	+	1.40860i	0.289668	+	0.957127i	$0.406455\pi$
$642$		0			0
$643$	−7.30455	−	1.28799i	−0.288063	−	0.0507933i	0.0277494	−	0.999615i	$-0.491166\pi$
$643$	−7.30455	−	1.28799i	−0.288063	−	0.0507933i	−0.315813	+	0.948822i	$0.602277\pi$
$644$		0			0
$645$	−30.4867	−	23.7542i	−1.20041	−	0.935320i
$646$		0			0
$647$	13.4394			0.528359			0.264180	−	0.964474i	$-0.414899\pi$
$647$	13.4394			0.528359			0.264180	+	0.964474i	$0.414899\pi$
$648$		0			0
$649$	−1.81301			−0.0711669
$650$		0			0
$651$	−4.29927	−	3.34985i	−0.168502	−	0.131291i
$652$		0			0
$653$	20.6649	+	3.64379i	0.808681	+	0.142592i	0.562678	−	0.826676i	$-0.309771\pi$
$653$	20.6649	+	3.64379i	0.808681	+	0.142592i	0.246004	+	0.969269i	$0.420882\pi$
$654$		0			0
$655$	−1.35823	−	1.61867i	−0.0530704	−	0.0632468i
$656$		0			0
$657$	29.4810	−	28.6199i	1.15016	−	1.11657i
$658$		0			0
$659$	6.93840	+	39.3496i	0.270282	+	1.53284i	0.753561	+	0.657378i	$0.228334\pi$
$659$	6.93840	+	39.3496i	0.270282	+	1.53284i	−0.483279	+	0.875466i	$0.660554\pi$
$660$		0			0
$661$	8.62964	−	3.14093i	0.335654	−	0.122168i	−0.168694	−	0.985668i	$-0.553955\pi$
$661$	8.62964	−	3.14093i	0.335654	−	0.122168i	0.504348	+	0.863500i	$0.331733\pi$
$662$		0			0
$663$	−8.95304	−	9.91706i	−0.347707	−	0.385147i
$664$		0			0
$665$	3.20104	+	1.84812i	0.124131	+	0.0716670i
$666$		0			0
$667$	9.35817	−	5.40294i	0.362350	−	0.209203i
$668$		0			0
$669$	0.566198	+	15.6237i	0.0218905	+	0.604045i
$670$		0			0
$671$	−3.49907	−	2.93607i	−0.135080	−	0.113346i
$672$		0			0
$673$	9.36707	+	3.40934i	0.361074	+	0.131420i	0.516186	−	0.856477i	$-0.327351\pi$
$673$	9.36707	+	3.40934i	0.361074	+	0.131420i	−0.155112	+	0.987897i	$0.549574\pi$
$674$		0			0
$675$	−5.55868	+	5.80190i	−0.213954	+	0.223315i
$676$		0			0
$677$	−13.1036	+	36.0019i	−0.503613	+	1.38366i	0.384111	+	0.923287i	$0.374508\pi$
$677$	−13.1036	+	36.0019i	−0.503613	+	1.38366i	−0.887723	+	0.460377i	$0.847714\pi$
$678$		0			0
$679$	0.521166	−	0.621101i	0.0200005	−	0.0238357i
$680$		0			0
$681$	−10.8158	+	20.4065i	−0.414464	+	0.781977i
$682$		0			0
$683$	−20.9774	−	36.3339i	−0.802677	−	1.39028i	−0.917848	−	0.396932i	$-0.870075\pi$
$683$	−20.9774	−	36.3339i	−0.802677	−	1.39028i	0.115171	−	0.993346i	$-0.463258\pi$
$684$		0			0
$685$	7.47669	−	12.9500i	0.285669	−	0.494794i
$686$		0			0
$687$	−14.9813	−	4.84592i	−0.571574	−	0.184883i
$688$		0			0
$689$	−0.931645	−	2.55967i	−0.0354928	−	0.0975158i
$690$		0			0
$691$	21.7535	−	3.83573i	0.827542	−	0.145918i	0.256194	−	0.966625i	$-0.417531\pi$
$691$	21.7535	−	3.83573i	0.827542	−	0.145918i	0.571349	+	0.820707i	$0.306420\pi$
$692$		0			0
$693$	−0.675119	−	0.327078i	−0.0256456	−	0.0124247i
$694$		0			0
$695$	7.72607	−	6.48295i	0.293067	−	0.245912i
$696$		0			0
$697$	−4.83472	+	27.4191i	−0.183128	+	1.03857i
$698$		0			0
$699$	−4.63879	−	11.4380i	−0.175455	−	0.432625i
$700$		0			0
$701$		−	27.1898i		−	1.02695i	−0.858106	−	0.513473i	$-0.828359\pi$
$701$		−	27.1898i		−	1.02695i	0.858106	−	0.513473i	$-0.171641\pi$
$702$		0			0
$703$		−	10.2651i		−	0.387157i
$704$		0			0
$705$	31.6949	+	4.41185i	1.19370	+	0.166160i
$706$		0			0
$707$	0.840115	−	4.76453i	0.0315958	−	0.179189i
$708$		0			0
$709$	34.1540	−	28.6586i	1.28268	−	1.07630i	0.289810	−	0.957084i	$-0.406408\pi$
$709$	34.1540	−	28.6586i	1.28268	−	1.07630i	0.992869	−	0.119211i	$-0.0380366\pi$
$710$		0			0
$711$	−22.0223	−	2.25599i	−0.825902	−	0.0846063i
$712$		0			0
$713$	8.18751	−	1.44368i	0.306625	−	0.0540662i
$714$		0			0
$715$	0.618029	+	1.69802i	0.0231130	+	0.0635024i
$716$		0			0
$717$	3.04232	+	14.2208i	0.113618	+	0.531087i
$718$		0			0
$719$	−21.5033	+	37.2448i	−0.801937	+	1.38900i	0.116403	+	0.993202i	$0.462864\pi$
$719$	−21.5033	+	37.2448i	−0.801937	+	1.38900i	−0.918340	+	0.395793i	$0.870470\pi$
$720$		0			0
$721$	3.17204	+	5.49414i	0.118133	+	0.204612i
$722$		0			0
$723$	−7.72544	−	12.3271i	−0.287312	−	0.458450i
$724$		0			0
$725$	−5.91806	+	7.05286i	−0.219791	+	0.261937i
$726$		0			0
$727$	−9.94324	+	27.3188i	−0.368775	+	1.01320i	0.607054	+	0.794661i	$0.292351\pi$
$727$	−9.94324	+	27.3188i	−0.368775	+	1.01320i	−0.975828	+	0.218539i	$0.929871\pi$
$728$		0			0
$729$	−18.2246	−	19.9215i	−0.674984	−	0.737833i
$730$		0			0
$731$	32.5835	+	11.8594i	1.20515	+	0.438637i
$732$		0			0
$733$	−12.0928	−	10.1471i	−0.446658	−	0.374791i	0.391536	−	0.920163i	$-0.371944\pi$
$733$	−12.0928	−	10.1471i	−0.446658	−	0.374791i	−0.838194	+	0.545372i	$0.816388\pi$
$734$		0			0
$735$	−17.8054	+	11.1587i	−0.656763	+	0.411595i
$736$		0			0
$737$	1.57901	−	0.911643i	0.0581637	−	0.0335808i
$738$		0			0
$739$	40.2356	+	23.2300i	1.48009	+	0.854531i	0.999746	−	0.0225487i	$-0.00717807\pi$
$739$	40.2356	+	23.2300i	1.48009	+	0.854531i	0.480345	+	0.877080i	$0.340511\pi$
$740$		0			0
$741$	−13.0990	+	2.80232i	−0.481203	+	0.102946i
$742$		0			0
$743$	−39.2909	+	14.3007i	−1.44144	+	0.524643i	−0.940188	−	0.340656i	$-0.889351\pi$
$743$	−39.2909	+	14.3007i	−1.44144	+	0.524643i	−0.501257	+	0.865299i	$0.667129\pi$
$744$		0			0
$745$	0.641552	+	3.63842i	0.0235047	+	0.133302i
$746$		0			0
$747$	1.18944	−	11.6109i	0.0435192	−	0.424821i
$748$		0			0
$749$	5.17694	+	6.16964i	0.189161	+	0.225434i
$750$		0			0
$751$	31.0407	+	5.47331i	1.13269	+	0.199724i	0.708406	−	0.705805i	$-0.249415\pi$
$751$	31.0407	+	5.47331i	1.13269	+	0.199724i	0.424284	+	0.905529i	$0.360526\pi$
$752$		0			0
$753$	−7.47329	+	53.6884i	−0.272342	+	1.95651i
$754$		0			0
$755$	5.33018			0.193985
$756$		0			0
$757$	11.5123			0.418421			0.209210	−	0.977871i	$-0.432911\pi$
$757$	11.5123			0.418421			0.209210	+	0.977871i	$0.432911\pi$
$758$		0			0
$759$	1.06043	−	0.430067i	0.0384911	−	0.0156104i
$760$		0			0
$761$	−27.5836	−	4.86373i	−0.999903	−	0.176310i	−0.350344	−	0.936621i	$-0.613935\pi$
$761$	−27.5836	−	4.86373i	−0.999903	−	0.176310i	−0.649559	+	0.760311i	$0.725047\pi$
$762$		0			0
$763$	−5.65125	−	6.73489i	−0.204589	−	0.243820i
$764$		0			0
$765$	−7.01991	+	14.4897i	−0.253805	+	0.523877i
$766$		0			0
$767$	2.31003	+	13.1009i	0.0834105	+	0.473044i
$768$		0			0
$769$	−25.9996	+	9.46309i	−0.937571	+	0.341248i	−0.765206	−	0.643785i	$-0.777363\pi$
$769$	−25.9996	+	9.46309i	−0.937571	+	0.341248i	−0.172365	+	0.985033i	$0.555141\pi$
$770$		0			0
$771$	11.1760	−	34.5510i	0.402494	−	1.24432i
$772$		0			0
$773$	37.0220	+	21.3747i	1.33159	+	0.768793i	0.985543	−	0.169425i	$-0.0541911\pi$
$773$	37.0220	+	21.3747i	1.33159	+	0.768793i	0.346045	+	0.938218i	$0.387524\pi$
$774$		0			0
$775$	−6.13454	+	3.54178i	−0.220359	+	0.127224i
$776$		0			0
$777$	−3.72700	−	1.97539i	−0.133705	−	0.0708666i
$778$		0			0
$779$	21.3838	+	17.9432i	0.766156	+	0.642881i
$780$		0			0
$781$	−5.67747	−	2.06643i	−0.203156	−	0.0739427i
$782$		0			0
$783$	−22.3396	−	21.4031i	−0.798352	−	0.764885i
$784$		0			0
$785$	−7.69419	+	21.1396i	−0.274617	+	0.754505i
$786$		0			0
$787$	−12.9543	+	15.4383i	−0.461769	+	0.550315i	−0.945806	−	0.324733i	$-0.894726\pi$
$787$	−12.9543	+	15.4383i	−0.461769	+	0.550315i	0.484037	+	0.875048i	$0.339170\pi$
$788$		0			0
$789$	−12.6757	+	0.459364i	−0.451266	+	0.0163538i
$790$		0			0
$791$	3.90889	+	6.77039i	0.138984	+	0.240727i
$792$		0			0
$793$	−16.7578	+	29.0253i	−0.595086	+	1.03072i
$794$		0			0
$795$	−2.43655	+	2.19969i	−0.0864154	+	0.0780151i
$796$		0			0
$797$	−17.2695	−	47.4474i	−0.611716	−	1.68067i	−0.726400	−	0.687273i	$-0.758808\pi$
$797$	−17.2695	−	47.4474i	−0.611716	−	1.68067i	0.114684	−	0.993402i	$-0.463414\pi$
$798$		0			0
$799$	−28.2741	+	4.98548i	−1.00027	+	0.176374i
$800$		0			0
$801$	−29.2255	−	30.1048i	−1.03263	−	1.06370i
$802$		0			0
$803$	3.81929	−	3.20477i	0.134780	−	0.113094i
$804$		0			0
$805$	−0.402319	+	2.28166i	−0.0141799	+	0.0804180i
$806$		0			0
$807$	−19.5480	+	25.0884i	−0.688124	+	0.883154i
$808$		0			0
$809$		−	9.20124i		−	0.323498i	−0.986832	−	0.161749i	$-0.948286\pi$
$809$		−	9.20124i		−	0.323498i	0.986832	−	0.161749i	$-0.0517135\pi$
$810$		0			0
$811$			11.4571i			0.402312i	0.979559	+	0.201156i	$0.0644697\pi$
$811$			11.4571i			0.402312i	−0.979559	+	0.201156i	$0.935530\pi$
$812$		0			0
$813$	−1.15048	+	1.47655i	−0.0403489	+	0.0517847i
$814$		0			0
$815$	−1.19105	+	6.75478i	−0.0417206	+	0.236610i
$816$		0			0
$817$	26.6316	−	22.3465i	0.931721	−	0.781807i
$818$		0			0
$819$	−1.50328	+	5.29517i	−0.0525288	+	0.185028i
$820$		0			0
$821$	6.64372	−	1.17147i	0.231867	−	0.0408845i	−0.0565070	−	0.998402i	$-0.517996\pi$
$821$	6.64372	−	1.17147i	0.231867	−	0.0408845i	0.288374	+	0.957518i	$0.406885\pi$
$822$		0			0
$823$	5.31714	+	14.6087i	0.185344	+	0.509228i	0.997213	−	0.0746118i	$-0.0237718\pi$
$823$	5.31714	+	14.6087i	0.185344	+	0.509228i	−0.811869	+	0.583840i	$0.801550\pi$
$824$		0			0
$825$	−0.723696	+	0.653347i	−0.0251959	+	0.0227466i
$826$		0			0
$827$	18.0772	−	31.3106i	0.628606	−	1.08878i	−0.359226	−	0.933251i	$-0.616959\pi$
$827$	18.0772	−	31.3106i	0.628606	−	1.08878i	0.987832	−	0.155527i	$-0.0497075\pi$
$828$		0			0
$829$	−7.04448	−	12.2014i	−0.244665	−	0.423772i	0.717373	−	0.696690i	$-0.245345\pi$
$829$	−7.04448	−	12.2014i	−0.244665	−	0.423772i	−0.962037	+	0.272918i	$0.912011\pi$
$830$		0			0
$831$	24.0706	−	0.872315i	0.835000	−	0.0302603i
$832$		0			0
$833$	12.1182	−	14.4419i	0.419871	−	0.500383i
$834$		0			0
$835$	13.1915	−	36.2434i	0.456512	−	1.25426i
$836$		0			0
$837$	−10.5190	−	21.3525i	−0.363589	−	0.738051i
$838$		0			0
$839$	−15.6165	−	5.68395i	−0.539142	−	0.196232i	0.0580737	−	0.998312i	$-0.481504\pi$
$839$	−15.6165	−	5.68395i	−0.539142	−	0.196232i	−0.597216	+	0.802081i	$0.703726\pi$
$840$		0			0
$841$	−4.94101	−	4.14600i	−0.170380	−	0.142965i
$842$		0			0
$843$	−8.59147	−	4.55366i	−0.295906	−	0.156836i
$844$		0			0
$845$	−9.44004	+	5.45021i	−0.324747	+	0.187493i
$846$		0			0
$847$	6.46498	+	3.73256i	0.222139	+	0.128252i
$848$		0			0
$849$	−8.71940	+	26.9563i	−0.299249	+	0.925139i
$850$		0			0
$851$	6.04631	−	2.20068i	0.207265	−	0.0754382i
$852$		0			0
$853$	−8.76180	−	49.6906i	−0.299998	−	1.70138i	−0.646161	−	0.763201i	$-0.723627\pi$
$853$	−8.76180	−	49.6906i	−0.299998	−	1.70138i	0.346163	−	0.938174i	$-0.387484\pi$
$854$		0			0
$855$	9.06206	+	13.3590i	0.309916	+	0.456868i
$856$		0			0
$857$	−25.4251	−	30.3005i	−0.868506	−	1.03504i	−0.999049	−	0.0436021i	$-0.986117\pi$
$857$	−25.4251	−	30.3005i	−0.868506	−	1.03504i	0.130543	−	0.991443i	$-0.458328\pi$
$858$		0			0
$859$	18.3052	+	3.22771i	0.624567	+	0.110128i	0.476970	−	0.878920i	$-0.341735\pi$
$859$	18.3052	+	3.22771i	0.624567	+	0.110128i	0.147597	+	0.989048i	$0.452846\pi$
$860$		0			0
$861$	10.6297	−	4.31099i	0.362260	−	0.146918i
$862$		0			0
$863$	35.2494			1.19990			0.599952	−	0.800036i	$-0.295187\pi$
$863$	35.2494			1.19990			0.599952	+	0.800036i	$0.295187\pi$
$864$		0			0
$865$	11.5913			0.394115
$866$		0			0
$867$	−2.06798	+	14.8564i	−0.0702321	+	0.504550i
$868$		0			0
$869$	−2.64542	−	0.466459i	−0.0897398	−	0.0158235i
$870$		0			0
$871$	−8.59944	−	10.2484i	−0.291381	−	0.347254i
$872$		0			0
$873$	3.23103	−	1.44876i	0.109354	−	0.0490331i
$874$		0			0
$875$	−1.45116	−	8.22996i	−0.0490583	−	0.278223i
$876$		0			0
$877$	−41.9724	+	15.2767i	−1.41731	+	0.515858i	−0.933266	−	0.359187i	$-0.883054\pi$
$877$	−41.9724	+	15.2767i	−1.41731	+	0.515858i	−0.484042	+	0.875045i	$0.660832\pi$
$878$		0			0
$879$	19.3031	−	4.12959i	0.651078	−	0.139288i
$880$		0			0
$881$	2.33653	+	1.34900i	0.0787198	+	0.0454489i	0.538843	−	0.842406i	$-0.318862\pi$
$881$	2.33653	+	1.34900i	0.0787198	+	0.0454489i	−0.460123	+	0.887855i	$0.652195\pi$
$882$		0			0
$883$	17.3880	−	10.0389i	0.585151	−	0.337837i	−0.178027	−	0.984026i	$-0.556971\pi$
$883$	17.3880	−	10.0389i	0.585151	−	0.337837i	0.763178	+	0.646188i	$0.223638\pi$
$884$		0			0
$885$	13.5840	−	8.51315i	0.456622	−	0.286166i
$886$		0			0
$887$	−17.5348	−	14.7135i	−0.588762	−	0.494030i	0.299049	−	0.954238i	$-0.403331\pi$
$887$	−17.5348	−	14.7135i	−0.588762	−	0.494030i	−0.887811	+	0.460208i	$0.847775\pi$
$888$		0			0
$889$	−7.71279	−	2.80723i	−0.258679	−	0.0941513i
$890$		0			0
$891$	−2.03064	−	2.57106i	−0.0680289	−	0.0861336i
$892$		0			0
$893$	−9.84507	+	27.0491i	−0.329453	+	0.905164i
$894$		0			0
$895$	−16.1680	+	19.2682i	−0.540436	+	0.644066i
$896$		0			0
$897$	−4.45881	−	7.11472i	−0.148875	−	0.237553i
$898$		0			0
$899$	−13.6372	−	23.6204i	−0.454828	−	0.787784i
$900$		0			0
$901$	1.47254	−	2.55052i	0.0490575	−	0.0849701i
$902$		0			0
$903$	−2.98855	−	13.9695i	−0.0994528	−	0.464876i
$904$		0			0
$905$	−4.31288	−	11.8495i	−0.143365	−	0.393892i
$906$		0			0
$907$	2.29373	−	0.404447i	0.0761621	−	0.0134294i	−0.135437	−	0.990786i	$-0.543244\pi$
$907$	2.29373	−	0.404447i	0.0761621	−	0.0134294i	0.211599	+	0.977356i	$0.432133\pi$
$908$		0			0
$909$	12.3743	−	17.1265i	0.410430	−	0.568050i
$910$		0			0
$911$	−1.41352	+	1.18609i	−0.0468320	+	0.0392968i	−0.665903	−	0.746038i	$-0.731954\pi$
$911$	−1.41352	+	1.18609i	−0.0468320	+	0.0392968i	0.619071	+	0.785335i	$0.287509\pi$
$912$		0			0
$913$	0.245933	−	1.39476i	0.00813920	−	0.0461597i
$914$		0			0
$915$	40.0035	+	5.56839i	1.32247	+	0.184085i
$916$		0			0
$917$		−	0.781039i		−	0.0257922i
$918$		0			0
$919$		−	7.95591i		−	0.262441i	−0.991353	−	0.131221i	$-0.958110\pi$
$919$		−	7.95591i		−	0.262441i	0.991353	−	0.131221i	$-0.0418896\pi$
$920$		0			0
$921$	4.66728	+	11.5083i	0.153792	+	0.379210i
$922$		0			0
$923$	−7.69816	+	43.6585i	−0.253388	+	1.43704i
$924$		0			0
$925$	−4.19962	+	3.52390i	−0.138083	+	0.115865i
$926$		0			0
$927$	2.00553	+	27.6339i	0.0658702	+	0.907616i
$928$		0			0
$929$	−33.5766	+	5.92047i	−1.10161	+	0.194244i	−0.694755	−	0.719247i	$-0.744487\pi$
$929$	−33.5766	+	5.92047i	−1.10161	+	0.194244i	−0.406859	+	0.913491i	$0.633376\pi$
$930$		0			0
$931$	−6.46477	−	17.7618i	−0.211874	−	0.582120i
$932$		0			0
$933$	−35.3269	−	11.4270i	−1.15655	−	0.374103i
$934$		0			0
$935$	−0.976848	+	1.69195i	−0.0319463	+	0.0553327i
$936$		0			0
$937$	25.5356	+	44.2290i	0.834213	+	1.44490i	0.894670	+	0.446728i	$0.147411\pi$
$937$	25.5356	+	44.2290i	0.834213	+	1.44490i	−0.0604570	+	0.998171i	$0.519256\pi$
$938$		0			0
$939$	5.91580	−	11.1614i	0.193055	−	0.364240i
$940$		0			0
$941$	−19.1713	+	22.8475i	−0.624968	+	0.744808i	−0.981916	−	0.189317i	$-0.939373\pi$
$941$	−19.1713	+	22.8475i	−0.624968	+	0.744808i	0.356948	+	0.934124i	$0.383817\pi$
$942$		0			0
$943$	−5.98444	+	16.4421i	−0.194880	+	0.535429i
$944$		0			0
$945$	6.59417	−	0.719436i	0.214508	−	0.0234032i
$946$		0			0
$947$	39.9500	+	14.5406i	1.29820	+	0.472507i	0.896411	−	0.443225i	$-0.146166\pi$
$947$	39.9500	+	14.5406i	1.29820	+	0.472507i	0.401791	+	0.915731i	$0.368388\pi$
$948$		0			0
$949$	−28.0240	−	23.5150i	−0.909699	−	0.763328i
$950$		0			0
$951$	1.45901	+	40.2597i	0.0473115	+	1.30551i
$952$		0			0
$953$	20.2227	−	11.6756i	0.655078	−	0.378209i	−0.135321	−	0.990802i	$-0.543207\pi$
$953$	20.2227	−	11.6756i	0.655078	−	0.378209i	0.790399	+	0.612592i	$0.209873\pi$
$954$		0			0
$955$	−26.3214	−	15.1967i	−0.851741	−	0.491753i
$956$		0			0
$957$	−2.51564	−	2.78651i	−0.0813192	−	0.0900752i
$958$		0			0
$959$	5.19389	−	1.89042i	0.167719	−	0.0610448i
$960$		0			0
$961$	1.73919	+	9.86344i	0.0561029	+	0.318175i
$962$		0			0
$963$	8.59920	+	34.1064i	0.277105	+	1.09906i
$964$		0			0
$965$	22.6434	+	26.9853i	0.728916	+	0.868688i
$966$		0			0
$967$	−33.8501	−	5.96869i	−1.08855	−	0.191940i	−0.399555	−	0.916709i	$-0.630835\pi$
$967$	−33.8501	−	5.96869i	−1.08855	−	0.191940i	−0.688992	+	0.724769i	$0.741947\pi$
$968$		0			0
$969$	−11.4244	−	8.90151i	−0.367005	−	0.285958i
$970$		0			0
$971$	−46.5628			−1.49427			−0.747136	−	0.664672i	$-0.768571\pi$
$971$	−46.5628			−1.49427			−0.747136	+	0.664672i	$0.768571\pi$
$972$		0			0
$973$	3.72797			0.119513
$974$		0			0
$975$	5.64319	+	4.39699i	0.180727	+	0.140816i
$976$		0			0
$977$	−53.9905	−	9.51998i	−1.72731	−	0.304571i	−0.780212	−	0.625516i	$-0.784889\pi$
$977$	−53.9905	−	9.51998i	−1.72731	−	0.304571i	−0.947098	+	0.320944i	$0.896000\pi$
$978$		0			0
$979$	−3.27258	−	3.90011i	−0.104592	−	0.124648i
$980$		0			0
$981$	−9.38705	−	37.2312i	−0.299706	−	1.18870i
$982$		0			0
$983$	5.28596	+	29.9782i	0.168596	+	0.956156i	0.945279	+	0.326264i	$0.105790\pi$
$983$	5.28596	+	29.9782i	0.168596	+	0.956156i	−0.776683	+	0.629892i	$0.783099\pi$
$984$		0			0
$985$	−41.1446	+	14.9754i	−1.31097	+	0.477156i
$986$		0			0
$987$	7.92627	+	8.77973i	0.252296	+	0.279462i
$988$		0			0
$989$	18.8718	+	10.8956i	0.600088	+	0.346461i
$990$		0			0
$991$	25.9511	−	14.9829i	0.824364	−	0.475946i	−0.0275554	−	0.999620i	$-0.508772\pi$
$991$	25.9511	−	14.9829i	0.824364	−	0.475946i	0.851919	+	0.523674i	$0.175439\pi$
$992$		0			0
$993$	−0.726501	−	20.0470i	−0.0230548	−	0.636173i
$994$		0			0
$995$	−17.8670	−	14.9922i	−0.566423	−	0.475286i
$996$		0			0
$997$	18.0596	+	6.57315i	0.571953	+	0.208174i	0.611773	−	0.791033i	$-0.290456\pi$
$997$	18.0596	+	6.57315i	0.571953	+	0.208174i	−0.0398208	+	0.999207i	$0.512679\pi$
$998$		0			0
$999$	−10.8869	−	14.8607i	−0.344447	−	0.470172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.c.239.2	yes	36
4.3	odd	2		432.2.be.b.239.5	yes	36
27.20	odd	18		432.2.be.b.47.5	✓	36
108.47	even	18	inner	432.2.be.c.47.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.5	✓	36	27.20	odd	18
432.2.be.b.239.5	yes	36	4.3	odd	2
432.2.be.c.47.2	yes	36	108.47	even	18	inner
432.2.be.c.239.2	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36628 - 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(0.441545 + 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +O(q^{10})\)	\(q+(-1.36628 - 1.06456i) q^{3} +(1.83017 + 0.322709i) q^{5} +(0.441545 + 0.526213i) q^{7} +(0.733433 + 2.90896i) q^{9} +(0.0632128 + 0.358498i) q^{11} +(2.50997 - 0.913554i) q^{13} +(-2.15698 - 2.38923i) q^{15} +(2.50099 + 1.44395i) q^{17} +(2.50751 - 1.44771i) q^{19} +(-0.0430893 - 1.18900i) q^{21} +(1.39029 + 1.16659i) q^{23} +(-1.45308 - 0.528877i) q^{25} +(2.09469 - 4.75524i) q^{27} +(2.03639 - 5.59492i) q^{29} +(2.94453 - 3.50915i) q^{31} +(0.295275 - 0.557101i) q^{33} +(0.638290 + 1.10555i) q^{35} +(1.77265 - 3.07032i) q^{37} +(-4.40185 - 1.42384i) q^{39} +(3.29740 + 9.05952i) q^{41} +(11.8245 - 2.08497i) q^{43} +(0.403559 + 5.56059i) q^{45} +(-7.61569 + 6.39032i) q^{47} +(1.13360 - 6.42896i) q^{49} +(-1.87989 - 4.63529i) q^{51} -1.01980i q^{53} +0.676511i q^{55} +(-4.96713 - 0.691413i) q^{57} +(-0.864840 + 4.90475i) q^{59} +(-9.61210 + 8.06551i) q^{61} +(-1.20689 + 1.67038i) q^{63} +(4.88848 - 0.861972i) q^{65} +(-1.71306 - 4.70659i) q^{67} +(-0.657619 - 3.07394i) q^{69} +(-8.29859 + 14.3736i) q^{71} +(-6.84801 - 11.8611i) q^{73} +(1.42229 + 2.26948i) q^{75} +(-0.160735 + 0.191556i) q^{77} +(-2.52383 + 6.93417i) q^{79} +(-7.92415 + 4.26706i) q^{81} +(-3.65593 - 1.33065i) q^{83} +(4.11127 + 3.44977i) q^{85} +(-8.73839 + 5.47637i) q^{87} +(-12.1121 + 6.99291i) q^{89} +(1.58899 + 0.917403i) q^{91} +(-7.75874 + 1.65986i) q^{93} +(5.05636 - 1.84037i) q^{95} +(-0.204961 - 1.16239i) q^{97} +(-0.996494 + 0.446818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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